"if you think childlike, you'll stay young. If you keep your energy going, and do everything with a little flair, you're gunna stay young. But most people do things without energy, and they atrophy their mind as well as their body. you have to think young, you have to laugh a lot, and you have to have good feelings for everyone in the world, because if you don't, it's going to come inside, your own poison, and it's over" Jerry Lewis
"I don’t believe
in the irreversibility of situations" Deleuze

Note on Citations

The numerical citations refer to page number. The source's text-space (including footnote region) is divided into four equal portions, a, b, c, d. If the citation is found in one such section, then for example it would be cited p.15c. If the cited text lies at a boundary, then it would be for example p.16cd. If it spans from one section to another, it is rendered either for example p.15a.d or p.15a-d. If it goes from a 'd' section and/or arrives at an 'a' section, the letters are omitted: p.15-16.

[Note: All boldface and underlining is my own. It is intended for skimming purposes. Bracketed comments are also my own explanations or interpretations.]

Henry Somers-Hall

Hegel, Deleuze, and the Critique of Representation.

Dialectics of Negation and Difference

Part 2: Responses to Representation

Chapter 4: The Virtual and the Actual

Subdivision 3: Depth in Deleuze and Merleau-Ponty

Very Brief Summary:

In his aesthetics, Merleau-Ponty creates an idea of depth that is like Bergson’s continuously integrated heterogeneous multiplicity and Deleuze’s difference as intensity. We see this depth in the way that variational lines and color in Klee and Cézanne generate the differential space of the painting. This differential generative aspect not visible in the work is like Deleuze’s virtual intensity, which explicates into extensity. Yet all objects are a mixture of virtual and actual.

Brief Summary:

In Merleau-Ponty’s later aesthetics, he articulates a concept of depth in painting that is like Bergson’s heterogeneous multiplicity. Before modern painting, special dimensions were something depicted, as if the objects filled a pregiven homogeneous Euclidean space. But with Cézanne and Klee, lines and color now generate space. On account of continuous variation, parts of the painting are continuously self-differentiating while remaining intrinsically related through these differential relations. It is like Bergson’s continuous heterogeneity. This for Merleau-Ponty is the real depth of the world that the painter depicts. It is the being of the world. and it is on the basis of this depth that spatial depth can be generated. For Cézanne and Klee, depth “is that which binds objects to one another, as the ground through which they interpenetrate”. (116) This fulfills Deleuze’s three criteria for the idea: this depth is not overtly sensible, it’s elements are reciprocally determined, and it is actualized in a multiplicity of spatio-temporal relations. This depth for Deleuze is the virtual intensive spatium, which is a multiplicity of continuous differential relations. The movement from virtual to actual produces the individual entities in extensity which may take on external relations (including opposition) and have an identity, but this was impossible while being intensities. This gives us a univocal rather than an equivocal sense of being. But all objects including artworks, which tend more toward the virtual, are composites of virtual and actual. For, if the object were completely actualized, it could be no further differentiated, and if it were purely virtual, there would be nothing actual to crystallize the system’s order. And when we bring into clarity the Idea, we confuse all the differential incompossible tendencies making it up.

Summary

Previously we saw how Deleuze’s Idea can be viewed in terms of topological phase space; for, it is multidimensional, non-sensible and non-conceptual, and it actualizes in various spatio-temporal relationships. Section two of this chapter was about the logic of multiplicities, and section three was about this new relation to science that the concept of heterogeneous multiplicity creates.

Now the third thing we will discuss in Bergson’s thought that Deleuze emphasizes is the method of intuition. It will allow us to see what happens between the two kinds of multiplicity. Deleuze’s concept of depth will show the how things happen in the middle ground between the two tendencies, and he draws from Merleau-Ponty’s later aesthetical writings. Here Merleau-Ponty’s concept of depth allows him to create a Bergsonian space, where space is not something fixed and external to the bodies in it. It is a generative theory of space. “Merleau-Ponty wishes to show that space and the object are generated at the same time, characterizing depth as that which brings the other dimensions into being.” (111) Deleuze takes up this concept of depth, and he considers it an intensive space. We can divide extensive space into homogeneous parts, but an intensity cannot be divided like this.

Dividing it in half leads to two quantities of water that behave similarly to the original quantity. Dividing the temperature of the system can change the nature of the system itself, however, as the behavior of the system becomes radically | altered once it passes through the various phase transitions. (111-112)

Intensity then is like Bergson’s duration, and it is unlike Euclidean space; rather it is more like virtual non-Euclidean space. Intensity is what actualizes the virtual, because it “allows the structure inherent in the virtual idea of the system to become an actual geometrical structure”. (112) The egg has extensive dimensions, but its development undergoes phase transitions, which are [somehow] alterations in intensity. “In this section we will therefore turn to Merleau-Ponty's aesthetics to clarify the role of the intensive. In order to incorporate it into our reading of Deleuze, we will first deal with two points. First, we will need to show that Merleau-Ponty's analysis is an ontological analysis, and second, that this ontology is fundamentally compatible with Deleuze's.” (112)

We begin with Merleau-Ponty’s Eye and Mind. Here he sees the artist disclosing the world in a way unlike how science does. A theory of painting for him is a metaphysics. Like with Bergson, Merleau-Ponty sees two ways of relating to the world. The scientists approach is operationalism, so she avoids dealing with the world’s properties directly and instead defines “concepts purely through our operations of measuring them, making science in this sense autonomous, since it deals simply with the correlation and analysis of data. In this approach, according to Merleau-Ponty, there is no longer any contact with the 'opacity of being,' which was present even in the early moments of modem science.” (112) Science is abstract. It renounces metaphysical questions | in order instead to characterize its success in terms of the manipulability of the object.” (112-113) The artist, however, has a nonmanipulative approach to the world. Yet the artist’s mind is not separate from the world. The essay explores how the artist opens the world, seeing how Renaissance geometrical perspective gives way to non-geometrical renditions in modern painting, beginning with Cézanne’s developments with depth. The essay does not want to renounce science but instead to give it the metaphysics it lacks. It also tries to give the transcendental grounds for perception, which is the invisible in the visible. (113)

We now consider parallels between the structures that Merleau-Ponty and Deleuze bring out.

[1] Painting’s action within space does not define what is painted.
The artist can actualize their Idea in various media, like painting, sculpture, drawing etc. This involves a move away from the spatio-temporal. [Each variation in a line is not just another point in a space but rather a new space for new self-relations, redefinitions.]

Within such a painting, each inflection of the line forms "another aspect of the line's relationship with itself, will form an adventure, a history, a meaning of the line" (EM, 183). Furthermore, when we ask what the nature of this line is, we find that it "is no longer the apparition of an entity upon a vacant background, as it was in classical geometry. It is, as in modem geometries, the restriction, segregation, or modulation of a pre-given spatiality" (EM, 1 84). [113]

This is like Deleuze’s Idea. “While the elements of the painting have sensible form, what is painted does not.” (114) Abstract art for Merleau-Ponty does not need to relate to some particular external state of affairs. It is only when the painter gives it a name that it takes on such a relation to a particular object or event. Like Deleuze’s Idea “its actualization is possible in a variety of contexts, depending on the relation the artist gives it to the visible.” (144) Also for Merleau-Ponty [and similar to Deleuze] the work itself convolutes space rather than occupies it, in that nonEuclidean, Riemannian, topological way. So Klee in Merleau-Ponty’s analysis meets Deleuze’s three criteria for Ideas. Klee’s lines do not tell us the sensible spatial dimensions of an object, but rather give us the lines continuous self-genesis. [It is like the development of an egg through intensive space rather than through extensive space.] Both the line and its space are reciprocally determined, meeting the second criteria. And because the painting with a different name would have different particular relations to objects and events, the painting can be actualized in many different contexts, meeting the third criteria.

For Descartes, we see the geometrical forms of things under deformation, in the way they hit our retinas. So squares take on the form of rectangles, for example [depending on the angle we view them. A cup saucer will be painted as an oval.] Paintings depict these deformations, and by doing so recreates a three-dimensional space. For Descartes, we perceive a third dimension merely from the two that are present in the painting. (114-115) Also note that we could imagine God’s eye located everywhere, thus there would be no visual depth, because depth is a relation between near and far. “In order for depth to be considered in this way, objects have to be conceived of as outside one another, with solid boundaries. The Cartesian approach therefore mirrors the approach of atomism in science that Bergson attacked” (115) Such a space is homogenous, always in itself, everywhere equal to itself, and its dimensions are interchangeable. (115)

But note how for Descartes, depth is produced through the two other dimensions in the painting. This production of space is important for Klee. “The strands of Sartre's critique of Kant, Klee's reworking of the concept of depth, and the work of Gauss and Riemann all therefore represent a move away from the classical paradigm of a homogeneous space to that of a Bergsonian interpenetrative multiplicity.” (115) Color for Klee is important, because it does not “give rise to the classical conception of space,” but rather “gives rise to an interpenetrative space exemplified by the late works of Cezanne.” (115) [Recall how Cézanne creates depth with color and not shading or modeling.'] “The idea of depth created by the color field differs from that of the brass etching in that the brass etching specifies depth as a third dimension, whereas for Cezanne | and Klee, depth is that which binds objects to one another, as the ground through which they interpenetrate”. (115-116) Depth then is “the first dimension that generates the others.Even the depth of the Cartesian geometry follows from this elementary depth.” (116) Merleau-Ponty sees Klee’s color in a way that is similar to Deleuze’s intensive qualities of the virtual. “That is, color cannot be divided without being changed in nature. Thus, the primordial dimension of depth for Merleau-Ponty is an intensive dimension. It is not color that is an intensity, but that which is more general than color, but can be captured by color's intensive nature.” (116)

Merleau-Ponty’s analyses of painting show us the actualization of intensive depth. [Depth is the movement of individuation, like the painted line that continually redefines itself and the space it generates through its movement. The creation of differentiation in general is the grounds for more specific sorts of differentiations, like the relations of different positions in extensive homogeneous space.]

Just as for Merleau-Ponty, depth generates the other dimensions, including Cartesian depth, for Deleuze, "extensity does not account for the individuations which occur within it" (DR, 229). That is, returning to Merleau-Ponty's analysis of the brass etchings of Descartes, extension itself both implies the already individuated in order to be generated, as Descartes sees the phenomenon of depth to be generated from the relations of bodies, and precludes the movement of individuation itself, since, from Bergson, the notion of a homogenous space renders an interpenetrative analysis impossible, as shown by the replacement of interpenetration with action at a distance in the work of Newton. Instead, Deleuze argues, "individuation and extensity must flow from a '"deeper' instance" (DR, 229). [116]

“Depth therefore forms the generative space from which extensive space | is generated.” (116-117) Deleuze calls this depth spatium. “Returning to Bergson, we can see that the spatium, as an interpenetrative multiplicity, functions for Deleuze like the multiplicity of duration.” (117) For Deleuze, “difference is that by which the given is given (DR, 222)” [117] The intensive field of depth is what gives the given. Difference is what is operating in this intensive field of depth. Intensity has a differential form [being made of a continuity of differential relations]. Actual diversity in the world is an explication of intensive difference.

For Deleuze, "difference is that by which the given is given" (DR, 222). That is, difference exists within the intensive field of depth, which is generative of extensity. In this sense, Deleuze calls it "the closest noumenon" (DR, 222). Thus, difference, as the differential form of intensity, gives rise to diversity by a process of explication. That is, as intensive force finds itself actualized within an extensive system, the unindividuated differential relations give way to relations between bodies external to one another. (117)

We will use differential calculus to understand the movement from virtual to actual. But for Deleuze and Bergson, there is not a logic of negation involved. [Negation and opposition are not a part of the intensive spatium, where multiplicities are intrinsically related differentially. They only come about in actualization into discrete entities. This is intrinsic differential relations inverted into extrinsic ones.]

Negation and opposition govern the state of the system as actualized and, therefore, for Deleuze, do indeed provide the limit case of the world in terms of the fully actual. "The negative is difference inverted, seen from below" (DR, 235). Likewise, the classical conception of identity, which requires individuation, is the result of the explication of differential relations into a spatiotemporal context. (117)

[Difference is a condition of possibility for actualization. (What is actualized are things we can understand.) So difference is transcendental. In Aristotle, being and beings were equivocal, because they had similar names but different meanings. Also note how each being is discrete from the others and externally differentiated from them. In the intensive spatium, there are no discrete beings. There is just difference, thoroughly expressed. So being is univocal, when being is difference. Also, Aristotle distinguished beings on account of oppositions between them. But since there is no opposition in the virtual, we can have a non-hierarchical understanding of being.]

In making difference the transcendental principle of his system, Deleuze has moved away from the principle of the equivocity of being put forward by Aristotle. The differential field of depth that forms the closest noumenon for Deleuze instead allows us to conceive of being as univocal. As the virtual is not defined in terms of opposition, it also allows the possibility of a nonhierarchical understanding of being, as the virtual is not to be understood in terms of opposition, which led to the theory of species and genera for Aristotle. (117)

But we need both the virtual and the actual to explain the givenness of the object [for, without the actualized object, nothing is being given, but without the virtual, nothing is giving the object.] For Merleau-Ponty, the work of art is between an actual thing and the intensive depth that generates things. Also for Deleuze, an artwork can be almost entirely virtual, displaying a “' ‘completely determined structure formed by its genetic differential elements"’ (DR, 209).” (108a) Yet for Deleuze all objects including artworks are double [expressing both virtual and actual] without the two halves resembling each other. In Descartes, an object’s clarity and distinctness are proportional. In Deleuze’s analysis of Leibniz’s sea example, we can have a clear perception of the sea’s white noise as a whole, but all our tiny perceptions of the different small splashings of water are confused with each other. If we try to focus on one small wave, we obtain a distinct perceptions of the differential relations [between tiny waves] that make up the whole, but our perception of the whole becomes obscure. “Thus the understanding of one kind of order within the murmuring of the sea covers the other.” (118)

For Deleuze, it is the Apolline of Nietzsche's Birth of Tragedy that provides the best expression of the clear-confused, as that tied to representation, whereas the distinct-obscure is the Dionysian and properly philosophical order of the object. It is thus Apollo who gives the power of representation, of actuality, to the object, while Dionysus provides the obscure genetic and virtual conditions of the object, and of its representation. For Deleuze, "the two never unite in order to reconstitute a natural light. Rather, they compose two languages which are encoded in the language of philosophy and directed at the divergent exercises of the faculties: the disparity of style" (DR, 214) In spite of this, however, an object can never achieve pure actuality, as this would mean that it would no longer be capable of being further differentiated, nor can it be pure virtuality, as pure virtuality would be without the grain of actuality around which the order of the actualized system can crystallize. [118]

We saw also that for Bergson, pure space and pure duration are impossibilities, even though they are implied in the directions of expansion and contraction of matter/duration. So for Deleuze, everything happens somewhere between pure virtuality and pure actuality. [Recall Deleuze’s Idea. In the topographical example, instead of drawing all the vectors, we instead create a surface showing the tendencies toward equilibria in the dynamics of the systems. So all the incompossible lines of development become confused together, when the Idea as a whole comes into greater clarity. Thus] “An Idea ‘is confused in so far as it is clear’ (DR, 213).” [118] Virtuality and actuality are like two languages in philosophy that are different in kind, but everything is a matter of degree between them. (118)